READ ME

The R script is designed for our manuscript entitled the external validation and clinical utility assessment of PREDICT breast cancer prognostic model in young women with node-negative breast cancer. This R script performed multiple imputation and run the PREDICT algorithms (version 2.2 and version 2.3) in order to calculate predicted risks for each individual in the study population. Using the script, we generated Table 2 of the manuscript.

library("readxl")
library("readr")
library("mice")
library("survival")
library("plyr")
library("tidyverse")
library("dplyr")
library("MASS")
library("VIM")
library("table1")
library("tidyr")

PARADIGM patients characterisitcs

#Dataset was loaded
columns<-c("palga_nr", # patient ID
           "T_LEEFT", #age at diagnosis
           "incyear", #incidence year
           "ER.num", #ER expression, 0 - 100%
           "ER.10", #categorical ER, based on 10%, positive vs. negative
           "er", #categorical ER, based on 1%, 1 vs. 0
           "PR.num", #PR expression, 0 - 100%
           "PR.10",#categorical PR, based on 10%, positive vs. negative
           "pr", #categorical PR, based on 1%, 1 vs. 0
           "HER2.cat", #categorical HER2, positive vs. negative
           "her2", #categorical her2, 1 vs. 0
           "TILs.cat4", #categorical TILs, absent, weak, moderate and strong
           "Grade",#categorical grade, grade 1, grade 2 and grade 3
           "grade", #categorical grade, 1, 2 and 3
           "size", # continuous tumor size
           "tumorsize.cat4", #categorical tumor size T1 to T3
           "push.border", # categorical pushing order "Absent", "<25%", "25%-75%", ">75%"
           "LVI", #lymphovascular invasion, 0 or 1
           "HISTOLOGICAL_SUBTYPErec", #histological subtypes
           "Radiotherapy", #yes or no
           "Surgery.cat3", #lumpactomy, mastectomy or surgery NNO
           "H.tilde",  #the Nelson-aalen estimator of the baseline hazard
           "delta", #death or not
           "time", #followup time
           "BCsubtype", #intrinsic subtype, based on ER (1%), PR (1%) and HER2
           "nodes" #positive nodal status, all 0
           )

PRD.final <- PRD %>%
  filter(T_LEEFT >= 25) %>% #remove women diagnosed under age 25
  dplyr::select(columns)
## Warning: Using an external vector in selections was deprecated in tidyselect 1.1.0.
## ℹ Please use `all_of()` or `any_of()` instead.
##   # Was:
##   data %>% select(columns)
## 
##   # Now:
##   data %>% select(all_of(columns))
## 
## See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
labels.table <- list(
  variables = list(T_LEEFT = "Age (years)",
                   er = "ER status",
                   pr = "PR status",
                   her2 = "HER2 status",
                   size = "Tumor size(mm)",
                   grade = "Tumor grade",
                   LVI = "LVI",
                   BCsubtype = "Immunohistochemical subtype",
                   Surgery.cat3 = "Surgery",
                   Radiotherapy = "Radiotherapy"),
  groups = list("", "ER stutus")
)
strata.table <- c(list(Total = PRD.final), split(PRD.final, PRD.final$er))


table1(strata.table, labels.table, groupspan=c(1, 2),
        render.continuous = "MEDIAN (Q1, Q3)",
       render.categorical = "FREQ (PCTnoNA%)")
ER stutus
Total
(N=2264)
0
(N=559)
1
(N=1379)
Age (years) 36.0 (33.0, 38.0) 35.0 (32.5, 38.0) 36.0 (34.0, 38.0)
ER status
0 559 (28.8%) 559 (100%) 0 (0%)
1 1379 (71.2%) 0 (0%) 1379 (100%)
Missing 326 (14.4%) 0 (0%) 0 (0%)
PR status
0 710 (36.7%) 531 (95.5%) 178 (12.9%)
1 1225 (63.3%) 25 (4.5%) 1199 (87.1%)
Missing 329 (14.5%) 3 (0.5%) 2 (0.1%)
HER2 status
0 1614 (83.3%) 465 (83.6%) 1145 (83.2%)
1 324 (16.7%) 91 (16.4%) 231 (16.8%)
Missing 326 (14.4%) 3 (0.5%) 3 (0.2%)
Tumor size(mm) 16.0 (12.0, 22.0) 20.0 (15.0, 25.0) 15.0 (12.0, 20.0)
Missing 324 (14.3%) 67 (12.0%) 165 (12.0%)
Tumor grade
1 367 (17.6%) 8 (1.4%) 337 (24.5%)
2 800 (38.4%) 97 (17.4%) 653 (47.4%)
3 917 (44.0%) 454 (81.2%) 387 (28.1%)
Missing 180 (8.0%) 0 (0%) 2 (0.1%)
LVI
0 1632 (82.4%) 486 (86.9%) 1118 (81.1%)
1 349 (17.6%) 73 (13.1%) 260 (18.9%)
Missing 283 (12.5%) 0 (0%) 1 (0.1%)
Immunohistochemical subtype
HR-HER2- 442 (22.9%) 442 (79.6%) 0 (0%)
HR-HER2+ 88 (4.6%) 88 (15.9%) 0 (0%)
HR+HER2- 1167 (60.4%) 22 (4.0%) 1145 (83.2%)
HR+HER2+ 235 (12.2%) 3 (0.5%) 231 (16.8%)
Missing 332 (14.7%) 4 (0.7%) 3 (0.2%)
Surgery
Lumpectomy 1410 (62.3%) 352 (63.0%) 881 (63.9%)
Mastectomy 811 (35.8%) 196 (35.1%) 474 (34.4%)
Surgery NNO 43 (1.9%) 11 (2.0%) 24 (1.7%)
Radiotherapy
No 754 (33.3%) 179 (32.0%) 442 (32.1%)
Yes 1510 (66.7%) 380 (68.0%) 937 (67.9%)
PRD.final %>%
  filter(delta == 0 & time < 10) %>%
  nrow(.)
## [1] 27
#27 women lost to FUP after 10 years

Multiple impuation

ER.num is a continuous variable. ER.cat.final was created based on the value of ER.num. If ER.num < 10%, ER.cat.final is negative, if ER.num >= 10%, ER.cat.final is positive. Besides, a binary ER status (10% cut-off) according to the registry from IKNL was used if ER.num was missing. However, in this project, we want to use 1% cut-off, which is widely used internationally. Therefore, we impute ER.num with a condition: if ER.cat.final is negative, then the imputed ER.num should be between 0 and 9; if ER.cat.final is positive, then the imputed ER.num should be between 10 and 100. This is achieved by post argument in the mice function.

We select age, incidence year, ER(continuous), PR(continuous), HER2, TILs, tumor grade, tumor size, pushing border, lymphovascular invasion, histological subtypes, radiotherapy, surgery, cumulative baseline hazard, and death to impute the missing values.

Missing patern

columns<-c("palga_nr","T_LEEFT","incyear","ER.num","ER.10","PR.num","PR.10","her2","HER2.cat",
           "TILs.cat4","Grade","grade", "size","tumorsize.cat4","push.border","LVI",
           "HISTOLOGICAL_SUBTYPErec","Radiotherapy","Surgery","H.tilde", "delta","time")

## Multiple imputation
data <- PRD[,columns] # select relevant columns

aggr(data, col=c('navyblue','red'), numbers=TRUE, sortVars=TRUE, labels=names(data), cex.axis=.7, gap=3, ylab=c("Histogram of missing","Pattern"))

## 
##  Variables sorted by number of missings: 
##                 Variable      Count
##                TILs.cat4 0.15485564
##              push.border 0.15398075
##                   PR.num 0.14479440
##                     size 0.14435696
##                   ER.num 0.14348206
##                     her2 0.14348206
##                 HER2.cat 0.14348206
##                      LVI 0.12467192
##                    Grade 0.07874016
##                    grade 0.07874016
##  HISTOLOGICAL_SUBTYPErec 0.01574803
##                 palga_nr 0.00000000
##                  T_LEEFT 0.00000000
##                  incyear 0.00000000
##                    ER.10 0.00000000
##                    PR.10 0.00000000
##           tumorsize.cat4 0.00000000
##             Radiotherapy 0.00000000
##                  Surgery 0.00000000
##                  H.tilde 0.00000000
##                    delta 0.00000000
##                     time 0.00000000

Conditions for imputation

ini <- mice(data, maxit=0, vis="monotone",print=FALSE) 
## Warning: Number of logged events: 4
# dry run: so that we have mice component generated and we can modify them 
meth <- ini$meth

pred <- quickpred(data, 
                exclude=c("palga_nr","ER.10","PR.10","HER2.cat","Grade", "tumorsize.cat4", "time"), 
                include = c("T_LEEFT", "incyear", "ER.num","PR.num", "her2", "size", "TILs.cat4", "grade",
                            "HISTOLOGICAL_SUBTYPErec","LVI","push.border","Radiotherapy","Surgery", 
                            "delta", "H.tilde"), 
                minpuc = 0.2, mincor = 0.125)

pred["ER.10",] <- 0
pred[,"ER.10"] <- 0

pred["PR.10",] <- 0
pred[,"PR.10"] <- 0

pred[,"HER2.cat"] <- 0
pred["HER2.cat",] <-0 

pred[,"Grade"] <- 0
pred["Grade",] <- 0

pred[,"tumorsize.cat4"] <- 0
pred["tumorsize.cat4",] <- 0

pred
##                         palga_nr T_LEEFT incyear ER.num ER.10 PR.num PR.10 her2
## palga_nr                       0       0       0      0     0      0     0    0
## T_LEEFT                        0       0       0      0     0      0     0    0
## incyear                        0       0       0      0     0      0     0    0
## ER.num                         0       1       1      0     0      1     0    1
## ER.10                          0       0       0      0     0      0     0    0
## PR.num                         0       1       1      1     0      0     0    1
## PR.10                          0       0       0      0     0      0     0    0
## her2                           0       1       1      1     0      1     0    0
## HER2.cat                       0       0       0      0     0      0     0    0
## TILs.cat4                      0       1       1      1     0      1     0    1
## Grade                          0       0       0      0     0      0     0    0
## grade                          0       1       1      1     0      1     0    1
## size                           0       1       1      1     0      1     0    1
## tumorsize.cat4                 0       0       0      0     0      0     0    0
## push.border                    0       1       1      1     0      1     0    1
## LVI                            0       1       1      1     0      1     0    1
## HISTOLOGICAL_SUBTYPErec        0       1       1      1     0      1     0    1
## Radiotherapy                   0       0       0      0     0      0     0    0
## Surgery                        0       0       0      0     0      0     0    0
## H.tilde                        0       0       0      0     0      0     0    0
## delta                          0       0       0      0     0      0     0    0
## time                           0       0       0      0     0      0     0    0
##                         HER2.cat TILs.cat4 Grade grade size tumorsize.cat4
## palga_nr                       0         0     0     0    0              0
## T_LEEFT                        0         0     0     0    0              0
## incyear                        0         0     0     0    0              0
## ER.num                         0         1     0     1    1              0
## ER.10                          0         0     0     0    0              0
## PR.num                         0         1     0     1    1              0
## PR.10                          0         0     0     0    0              0
## her2                           0         1     0     1    1              0
## HER2.cat                       0         0     0     0    0              0
## TILs.cat4                      0         0     0     1    1              0
## Grade                          0         0     0     0    0              0
## grade                          0         1     0     0    1              0
## size                           0         1     0     1    0              0
## tumorsize.cat4                 0         0     0     0    0              0
## push.border                    0         1     0     1    1              0
## LVI                            0         1     0     1    1              0
## HISTOLOGICAL_SUBTYPErec        0         1     0     1    1              0
## Radiotherapy                   0         0     0     0    0              0
## Surgery                        0         0     0     0    0              0
## H.tilde                        0         0     0     0    0              0
## delta                          0         0     0     0    0              0
## time                           0         0     0     0    0              0
##                         push.border LVI HISTOLOGICAL_SUBTYPErec Radiotherapy
## palga_nr                          0   0                       0            0
## T_LEEFT                           0   0                       0            0
## incyear                           0   0                       0            0
## ER.num                            1   1                       1            1
## ER.10                             0   0                       0            0
## PR.num                            1   1                       1            1
## PR.10                             0   0                       0            0
## her2                              1   1                       1            1
## HER2.cat                          0   0                       0            0
## TILs.cat4                         1   1                       1            1
## Grade                             0   0                       0            0
## grade                             1   1                       1            1
## size                              1   1                       1            1
## tumorsize.cat4                    0   0                       0            0
## push.border                       0   1                       1            1
## LVI                               1   0                       1            1
## HISTOLOGICAL_SUBTYPErec           1   1                       0            1
## Radiotherapy                      0   0                       0            0
## Surgery                           0   0                       0            0
## H.tilde                           0   0                       0            0
## delta                             0   0                       0            0
## time                              0   0                       0            0
##                         Surgery H.tilde delta time
## palga_nr                      0       0     0    0
## T_LEEFT                       0       0     0    0
## incyear                       0       0     0    0
## ER.num                        1       1     1    0
## ER.10                         0       0     0    0
## PR.num                        1       1     1    0
## PR.10                         0       0     0    0
## her2                          1       1     1    0
## HER2.cat                      0       0     0    0
## TILs.cat4                     1       1     1    0
## Grade                         0       0     0    0
## grade                         1       1     1    0
## size                          1       1     1    0
## tumorsize.cat4                0       0     0    0
## push.border                   1       1     1    0
## LVI                           1       1     1    0
## HISTOLOGICAL_SUBTYPErec       1       1     1    0
## Radiotherapy                  0       0     0    0
## Surgery                       0       0     0    0
## H.tilde                       0       0     0    0
## delta                         0       0     0    0
## time                          0       0     0    0
#these are ordered variable, I need to specify:
meth[c("TILs.cat4", "push.border", "grade")] = "polr" #proportional odds model for ordered data


post<-ini$post
post["ER.num"] <-"imp[[j]][data$ER.10[!r[,j]]==0, i] <- squeeze(imp[[j]][data$ER.10[!r[,j]]==0, i], c(0,9));
imp[[j]][data$ER.10[!r[,j]]==1, i] <- squeeze(imp[[j]][data$ER.10[!r[,j]]==1, i], c(10,100))"

post["PR.num"] <-"imp[[j]][data$PR.10[!r[,j]]==0, i] <- squeeze(imp[[j]][data$PR.10[!r[,j]]==0, i], c(0,9));
imp[[j]][data$PR.10[!r[,j]]==1, i] <- squeeze(imp[[j]][data$PR.10[!r[,j]]==1, i], c(10,100))"

post["size"] <-"imp[[j]][data$tumorsize.cat4[!r[,j]]==1, i] <- squeeze(imp[[j]][data$tumorsize.cat4[!r[,j]]==1, i], c(0,20));
imp[[j]][data$tumorsize.cat4[!r[,j]]==2, i] <- squeeze(imp[[j]][data$tumorsize.cat4[!r[,j]]==2, i], c(21,50));
imp[[j]][data$tumorsize.cat4[!r[,j]]==3, i] <- squeeze(imp[[j]][data$tumorsize.cat4[!r[,j]]==3, i], c(50,200))"

Imputation

## Impute
seed <- 11200 # to reproduce results
impute <- mice(data=data, m=50, seed=seed, meth=meth, pred=pred, maxit=20, post = post, vis="monotone")
## 
##  iter imp variable
##   1   1  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   2  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   3  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   4  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   5  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   6  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   7  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   8  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   9  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   10  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   11  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   12  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   13  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   14  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   15  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   16  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   17  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   18  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   19  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   20  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   21  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   22  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   23  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   24  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   25  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   26  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   27  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   28  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   29  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   30  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   31  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   32  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   33  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   34  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   35  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   36  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   37  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   38  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   39  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   40  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   41  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   42  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   43  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   44  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   45  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   46  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   47  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   48  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   49  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   1   50  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   1  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   2  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   3  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   4  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   5  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   6  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   7  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   8  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   9  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   10  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   11  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   12  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
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##   2   21  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   22  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   23  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   24  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   25  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   2   26  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
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##   20   35  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   36  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   37  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   38  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   39  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   40  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   41  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   42  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   43  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   44  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   45  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   46  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   47  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   48  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   49  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
##   20   50  grade  LVI  ER.num  her2  size  PR.num  push.border  TILs.cat4
## Warning: Number of logged events: 2
dataimpute <- mice::complete(impute, "long", FALSE)#False indicated that I don't want the orignial dataset included into dataimpute

#check conditional imputation
dataimpute %>%
  group_by(tumorsize.cat4) %>%
  summarise(max = max(size), min = min(size))
## # A tibble: 5 × 3
##   tumorsize.cat4   max   min
##            <dbl> <dbl> <dbl>
## 1              1    20     1
## 2              2    50    21
## 3              3   140    50
## 4              4    63     2
## 5            999    60     1
dataimpute %>%
  group_by(ER.10) %>%
  summarise(max = max(ER.num), min = min(ER.num))
## # A tibble: 3 × 3
##   ER.10   max   min
##   <dbl> <dbl> <dbl>
## 1     0     9     0
## 2     1   100    10
## 3   999   100     0
dataimpute %>%
  group_by(PR.10) %>%
  summarise(max = max(PR.num), min = min(PR.num))
## # A tibble: 3 × 3
##   PR.10   max   min
##   <dbl> <dbl> <dbl>
## 1     0     9     0
## 2     1   100    10
## 3   999   100     0
#check if it is converged
plot(impute, c("ER.num","PR.num","her2","grade","TILs.cat4","push.border","LVI","size"))

#the plot looks OK

densityplot(impute,data =~ size)

densityplot(impute,data =~ PR.num)

densityplot(impute,data =~ ER.num)

densityplot(impute,data =~ her2)

densityplot(impute,data =~ TILs.cat4)

densityplot(impute,data =~ grade)

densityplot(impute,data =~ push.border)

densityplot(impute,data =~ LVI)

### Percentage after MI

labels.table <- list(
  variables = list(T_LEEFT = "Age (years)",
                   er = "ER status",
                   pr = "PR status",
                   her2 = "HER2 status",
                   size = "Tumor size(mm)",
                   grade = "Tumor grade",
                   LVI = "LVI",
                   BCsubtype = "Immunohistochemical subtype",
                   Surgery.cat3 = "Surgery",
                   Radiotherapy = "Radiotherapy"),
  groups = list("", "ER stutus"))

dataimpute.final <- dataimpute %>%
  filter(T_LEEFT >= 25) %>%
  mutate(er = factor(ifelse(ER.num == 0, 0, 
                          ifelse(ER.num > 0, 1, NA))),
         pr = factor(ifelse(PR.num == 0, 0, 
                          ifelse(PR.num > 0, 1, NA))),
         her2 = factor(her2),
         grade = factor(grade),
         LVI = factor(LVI),
         TILs.cat4 = factor(TILs.cat4),
         Surgery.cat3 = factor(ifelse(str_detect(Surgery, "lumpectomy"), "Lumpectomy",
                               ifelse(str_detect(Surgery, "mastectomy"), "Mastectomy", "Surgery NNO")))) %>%
  mutate(BCsubtype = ifelse((er == 1| pr == 1) & her2 == 0, "HR+HER2-",
                        ifelse((er == 1| pr == 1) & her2 == 1, "HR+HER2+",
                          ifelse(er == 0 & pr == 0 & her2 == 1, "HR-HER2+",
                            ifelse(er == 0 & pr == 0 & her2 == 0, "HR-HER2-", NA)))))

strata.table <- c(list(Total = dataimpute.final), split(dataimpute.final, dataimpute.final$er))


table1(strata.table, labels.table, groupspan=c(1, 2),
        render.continuous = "MEDIAN (Q1, Q3)",
       render.categorical = "PCT%")
ER stutus
Total
(N=113200)
0
(N=32432)
1
(N=80768)
Age (years) 36.0 (33.0, 38.0) 35.0 (32.0, 38.0) 36.0 (34.0, 38.0)
ER status
0 28.7% 100% 0%
1 71.3% 0% 100%
PR status
0 36.5% 94.4% 13.3%
1 63.5% 5.6% 86.7%
HER2 status
0 83.2% 82.9% 83.3%
1 16.8% 17.1% 16.7%
Tumor size(mm) 17.0 (12.0, 21.0) 20.0 (15.0, 25.0) 15.0 (12.0, 20.0)
Tumor grade
1 17.7% 1.5% 24.2%
2 38.5% 16.5% 47.3%
3 43.8% 82.0% 28.5%
LVI
0 82.4% 86.5% 80.8%
1 17.6% 13.5% 19.2%
Immunohistochemical subtype
HR-HER2- 22.3% 78.0% 0%
HR-HER2+ 4.7% 16.4% 0%
HR+HER2- 60.8% 4.9% 83.3%
HR+HER2+ 12.1% 0.7% 16.7%
Surgery
Lumpectomy 62.3% 61.8% 62.5%
Mastectomy 35.8% 36.2% 35.7%
Surgery NNO 1.9% 2.0% 1.8%
Radiotherapy
No 33.3% 33.3% 33.3%
Yes 66.7% 66.7% 66.7%
Nr.ER <- as.data.frame(table(dataimpute.final$.imp, dataimpute.final$er))
median(Nr.ER$Freq[which(Nr.ER$Var2 == 0)])#649.5
## [1] 649.5
median(Nr.ER$Freq[which(Nr.ER$Var2 == 1)])#1614.5
## [1] 1614.5
Nr.subtype <- as.data.frame(table(dataimpute.final$.imp, dataimpute.final$BCsubtype))
median(Nr.subtype$Freq[which(Nr.subtype$Var2 == "HR+HER2-")])#1376
## [1] 1376
median(Nr.subtype$Freq[which(Nr.subtype$Var2 == "HR+HER2+")])#274
## [1] 274
median(Nr.subtype$Freq[which(Nr.subtype$Var2 == "HR-HER2+")])#106
## [1] 106
median(Nr.subtype$Freq[which(Nr.subtype$Var2 == "HR-HER2-")])#506
## [1] 505.5

PREDICT v2.2

Prepare for running PREDICT script

PREDICT needs information on age, ER, PR, HER2, tumor grade, tumor size, nodes, ki67, screening detected or not, and adjuvant treatment. In the PARADIGM, all patients had negative nodes, therefore, nodes are zero; all patients were diagnosed under 40, therefore, all patients were detected from clinic; all patients are systemic therapy-naive, therefore, treatment should be negative.

dataimpute.v22 <- dataimpute %>%
  mutate(er = factor(ifelse(ER.num == 0, 0, 
                          ifelse(ER.num > 0, 1, NA))),
         pr = factor(ifelse(PR.num == 0, 0, 
                          ifelse(PR.num > 0, 1, NA))),
         age.start = T_LEEFT,
         nodes = 0,
         screen = 0,
         ki67 = 9,
         generation = 0,
         horm = 0,
         traz = 0,
         bis = 0,
         timeyr = time,
         Surgery.cat3 = factor(ifelse(str_detect(Surgery, "lumpectomy"), "Lumpectomy",
                               ifelse(str_detect(Surgery, "mastectomy"), "Mastectomy", "Surgery NNO")))) %>%
  dplyr::select(- time) 

Run PREDICT V2.2

Note that PREDICTv2.2 published on https://github.com/gmp26/v22/blob/master/R/v22_model.R was slightly different. 1. PREDICTv2.2 allows missing values in grade (if missing, impute missingness with 2.13) and screening (if missing, impute missingness with 0.204). In my script, grade is not allowed to be missing, the same as the PREDICT published on their website. For screening, we expect very few women in our cohort who would undergo screening, as they were all under 40 years at diagnosis. Screening for BRCA1/2 carriers was not yet inplemented before 2000. 2. PREDICTv2.2 on the github added several codes about radiotherapy. However, these codes are currently disabled thus not being used right now. 3. PREDICTv2.2 on the github included systemic treatment. I deleted these part because all women in our cohort were adjuvant treatment-naive.

#calculate PI and predicted outcomes based on the PREDICT version 2.2
names(dataimpute.v22)
##  [1] ".imp"                    ".id"                    
##  [3] "palga_nr"                "T_LEEFT"                
##  [5] "incyear"                 "ER.num"                 
##  [7] "ER.10"                   "PR.num"                 
##  [9] "PR.10"                   "her2"                   
## [11] "HER2.cat"                "TILs.cat4"              
## [13] "Grade"                   "grade"                  
## [15] "size"                    "tumorsize.cat4"         
## [17] "push.border"             "LVI"                    
## [19] "HISTOLOGICAL_SUBTYPErec" "Radiotherapy"           
## [21] "Surgery"                 "H.tilde"                
## [23] "delta"                   "er"                     
## [25] "pr"                      "age.start"              
## [27] "nodes"                   "screen"                 
## [29] "ki67"                    "generation"             
## [31] "horm"                    "traz"                   
## [33] "bis"                     "timeyr"                 
## [35] "Surgery.cat3"
for (n in 1:nrow(dataimpute.v22)) {
  # Input case characteristics
  age.start  <- dataimpute.v22$age.start[n] #25 to 85
  screen     <- dataimpute.v22$screen[n]     # Clinically detected = 0, screen detected = 1
  size       <- dataimpute.v22$size[n]   # Tumour size mm
  grade      <- dataimpute.v22$grade[n]     # Tumour grade
  nodes      <- dataimpute.v22$nodes[n]     # Number positive nodes. Nodal micrometastases = 0.5
  er         <- dataimpute.v22$er[n]     # ER+ = 1, ER- = 0
  her2       <- dataimpute.v22$her2[n]     # HER2+ = 1, HER2- = 0, missing = 9
  ki67       <- dataimpute.v22$ki67[n]     # KI67+ = 1, KI67- = 0, missing = 9
  generation <- dataimpute.v22$generation[n]     # Chemo generation 0, 2 or 3 only
  horm       <- dataimpute.v22$horm[n]     # Hormone therapy Yes = 1, no = 0
  traz       <- dataimpute.v22$traz[n]    # Trastuzumab therapy Yes = 1, no = 0
  bis        <- dataimpute.v22$bis[n]     # Bisphosphonate therapy Yes = 1, no = 0

  # Grade variable for ER neg
  grade.val <- ifelse(er==1, grade, ifelse(grade==1, 0, 1))

  # Generate the coefficients
  age.mfp.1   <- ifelse(er==1, (age.start/10)^-2-.0287449295, age.start-56.3254902)
  age.beta.1  <- ifelse(er==1, 34.53642, 0.0089827)
  age.mfp.2   <- ifelse(er==1, (age.start/10)^-2*log(age.start/10)-.0510121013, 0)
  age.beta.2  <- ifelse(er==1, -34.20342, 0)
  size.mfp    <- ifelse(er==1, log(size/100)+1.545233938, (size/100)^.5-.5090456276)
  size.beta   <- ifelse(er==1, 0.7530729, 2.093446)
  nodes.mfp   <- ifelse(er==1,log((nodes+1)/10)+1.387566896,
                        log((nodes+1)/10)+1.086916249)
  nodes.beta  <- ifelse(er==1, 0.7060723, .6260541)
  grade.beta  <- ifelse(er==1, 0.746655, 1.129091)
  screen.beta <- ifelse(er==1, -0.22763366, 0)
  her2.beta   <- ifelse(her2==1, 0.2413,
                        ifelse(her2==0, -0.0762, 0))
  ki67.beta   <- ifelse(ki67==1 & er==1, 0.14904,
                        ifelse(ki67==0 & er==1, -0.1133, 0))

  # Calculate the other and breast mortality indicies

  # Other mortality prognostic index (mi)
  mi <- 0.0698252*((age.start/10)^2-34.23391957)

  # Breast cancer mortality prognostic index (v22)
  pi <- age.beta.1*age.mfp.1 + age.beta.2*age.mfp.2 + size.beta*size.mfp +
    nodes.beta*nodes.mfp + grade.beta*grade.val + screen.beta*screen +
    her2.beta + ki67.beta

  # Non breast cancer mortality
  # Generate cumulative baseline other mortality

  time<-c(5,10,15)

  base.m.cum.oth <- exp(-6.052919 + (1.079863*log(time)) + (.3255321*time^.5))


  # Generate cumulative survival non-breast mortality
  #YW: cumulative non-breast cancer survival
  s.cum.oth <- exp(-exp(mi)*base.m.cum.oth)

  # Generate annual survival from cumulative survival
  #YW: cumulative non-breast cancer mortality
  m.cum.oth <- 1 - s.cum.oth

  # Breast cancer specific mortality
  # Generate cumulative baseline breast mortality
  if (er==1) {
    base.m.cum.br <- exp(0.7424402 - 7.527762/time^.5 - 1.812513*log(time)/time^.5)
  } else { base.m.cum.br <- exp(-1.156036 + 0.4707332/time^2 - 3.51355/time)
  }
  # Calculate the cumulative breast cancer survival
  s.cum.br <- exp(-exp(pi)*base.m.cum.br)
  m.cum.br <- 1 - s.cum.br

  # All cause mortality
  m.cum.all <- 1 - s.cum.oth*s.cum.br
  #s.cum.all <- 100-100*m.cum.all

  # Proportion of all cause mortality that is breast cancer
  prop.br <- m.cum.br/(m.cum.br+m.cum.oth)
  prop.oth <- m.cum.oth/(m.cum.br+m.cum.oth)
  # Predicted cumulative breast specific mortality
  pred.m.br    <- prop.br*m.cum.all
  # Predicted cumulative non-breast cancer mortality
  pred.m.oth <- prop.oth*m.cum.all
  # Predicted cumulative all-cause mortality
  pred.all <- pred.m.br + pred.m.oth #pred.all=m.cum.all
  #dataimpute$br[n] <- pred.m.br  # Predicted breast cancer mortality
  #dataimpute$oth[n] <- pred.m.oth # Predicted non-breast cancer mortality
  # Predicted all cause mortality
  dataimpute.v22$s.cum.br5[n] <- s.cum.br[1]
  dataimpute.v22$s.cum.br10[n] <- s.cum.br[2]
  dataimpute.v22$s.cum.br15[n] <- s.cum.br[3]

  dataimpute.v22$s.cum.oth5[n] <- s.cum.oth[1]
  dataimpute.v22$s.cum.oth10[n] <- s.cum.oth[2]
  dataimpute.v22$s.cum.oth15[n] <- s.cum.oth[3]

  dataimpute.v22$all5[n] <- pred.all[1]
  dataimpute.v22$all10[n] <- pred.all[2]
  dataimpute.v22$all15[n] <- pred.all[3]


  #prognostic index, this is not related to time
  dataimpute.v22$pi[n] <- pi #larger pi is associated with higher risks of events

}
#calculate the predicted 10 years survival using PREDICT! v2.2:
dataimpute.v22<- dataimpute.v22 %>%
  mutate(predsurv5 = 1 - all5,
         predsurv10 = 1 - all10,
         predsurv15 = 1 - all15)

PREDICT v2.3

Prepare for running PREDICT script

dataimpute.v23 <- dataimpute %>%
  mutate(er = factor(ifelse(ER.num == 0, 0, 
                          ifelse(ER.num > 0, 1, NA))),
         pr = factor(ifelse(PR.num == 0, 0, 
                          ifelse(PR.num > 0, 1, NA))),
         age.start = T_LEEFT,
         nodes = 0,
         screen = 0,
         ki67 = 9,
         generation = 0,
         horm = 0,
         traz = 0,
         bis = 0,
         timeyr = time,
         Surgery.cat3 = factor(ifelse(str_detect(Surgery, "lumpectomy"), "Lumpectomy",
                               ifelse(str_detect(Surgery, "mastectomy"), "Mastectomy", "Surgery NNO")))) %>%
  dplyr::select(- time) 

Run PREDICT V2.3

PREDICT v2.3 was not yet published. The information on the predictor PR was derived from the manuscript from Grootes et al. 2022.

for (n in 1:nrow(dataimpute.v23)) {
  # Input case characteristics
  age.start  <- dataimpute.v23$age.start[n]
  screen     <- dataimpute.v23$screen[n]     # Clinically detected = 0, screen detected = 1
  size       <- dataimpute.v23$size[n]   # Tumour size mm
  grade      <- dataimpute.v23$grade[n]     # Tumour grade
  nodes      <- dataimpute.v23$nodes[n]     # Number positive nodes. Nodal micrometastases = 0.5
  er         <- dataimpute.v23$er[n]     # ER+ = 1, ER- = 0
  her2       <- dataimpute.v23$her2[n]     # HER2+ = 1, HER2- = 0, missing = 9
  ki67       <- dataimpute.v23$ki67[n]     # KI67+ = 1, KI67- = 0, missing = 9
  generation <- dataimpute.v23$generation[n]     # Chemo generation 0, 2 or 3 only
  horm       <- dataimpute.v23$horm[n]     # Hormone therapy Yes = 1, no = 0
  traz       <- dataimpute.v23$traz[n]    # Trastuzumab therapy Yes = 1, no = 0
  bis        <- dataimpute.v23$bis[n]     # Bisphosphonate therapy Yes = 1, no = 0
  pr         <- dataimpute.v23$pr[n] 
  
  # Grade variable for ER neg
  grade.val <- ifelse(er==1, grade, ifelse(grade==1, 0, 1))

  # Generate the coefficients
  age.mfp.1   <- ifelse(er==1, (age.start/10)^-2-.0287449295, age.start-56.3254902)
  age.beta.1  <- ifelse(er==1, 34.53642, 0.0089827)
  age.mfp.2   <- ifelse(er==1, (age.start/10)^-2*log(age.start/10)-.0510121013, 0)
  age.beta.2  <- ifelse(er==1, -34.20342, 0)
  size.mfp    <- ifelse(er==1, log(size/100)+1.545233938, (size/100)^.5-.5090456276)
  size.beta   <- ifelse(er==1, 0.7530729, 2.093446)
  nodes.mfp   <- ifelse(er==1,log((nodes+1)/10)+1.387566896,
                        log((nodes+1)/10)+1.086916249)
  nodes.beta  <- ifelse(er==1, 0.7060723, .6260541)
  grade.beta  <- ifelse(er==1, 0.746655, 1.129091)
  screen.beta <- ifelse(er==1, -0.22763366, 0)
  her2.beta   <- ifelse(her2==1, 0.2413,
                        ifelse(her2==0, -0.0762, 0))
  ki67.beta   <- ifelse(ki67==1 & er==1, 0.14904,
                        ifelse(ki67==0 & er==1, -0.1133, 0))
  pr.beta     <- ifelse(pr == 1 & er == 1, -0.0618754,
                        ifelse(pr == 0 & er == 1, 0.2623643,
                               ifelse(pr == 1 & er == 0, -0.2231436, 0.0295588)))
  
  # Other mortality prognostic index (mi)
  mi <- 0.0698252*((age.start/10)^2-34.23391957)

  # Breast cancer mortality prognostic index (pi)
  pi <- age.beta.1*age.mfp.1 + age.beta.2*age.mfp.2 + size.beta*size.mfp +
    nodes.beta*nodes.mfp + grade.beta*grade.val + screen.beta*screen +
    her2.beta + ki67.beta + pr.beta

  # Non breast cancer mortality
  # Generate cumulative baseline other mortality

  time<-c(5,10,15)

  base.m.cum.oth <- exp(-6.052919 + (1.079863*log(time)) + (.3255321*time^.5))


  # Generate cumulative survival non-breast mortality
  #YW: cumulative non-breast cancer survival
  s.cum.oth <- exp(-exp(mi)*base.m.cum.oth)

  # Generate annual survival from cumulative survival
  #YW: cumulative non-breast cancer mortality
  m.cum.oth <- 1 - s.cum.oth

  # Breast cancer specific mortality
  # Generate cumulative baseline breast mortality
  if (er==1) {
    base.m.cum.br <- exp(0.7424402 - 7.527762/time^.5 - 1.812513*log(time)/time^.5)
  } else { base.m.cum.br <- exp(-1.156036 + 0.4707332/time^2 - 3.51355/time)
  }
  # Calculate the cumulative breast cancer survival
  s.cum.br <- exp(-exp(pi)*base.m.cum.br)
  m.cum.br <- 1 - s.cum.br

  # All cause mortality
  m.cum.all <- 1 - s.cum.oth*s.cum.br
  s.cum.all <- 100-100*m.cum.all

  # Proportion of all cause mortality that is breast cancer
  prop.br <- m.cum.br/(m.cum.br+m.cum.oth)
  prop.oth <- m.cum.oth/(m.cum.br+m.cum.oth)
  # Predicted cumulative breast specific mortality
  pred.m.br    <- prop.br*m.cum.all
  # Predicted cumulative non-breast cancer mortality
  pred.m.oth <- prop.oth*m.cum.all
  # Predicted cumulative all-cause mortality
  pred.all <- pred.m.br + pred.m.oth #pred.all=m.cum.all
  #dataimpute$br[n] <- pred.m.br  # Predicted breast cancer mortality
  #dataimpute$oth[n] <- pred.m.oth # Predicted non-breast cancer mortality
  # Predicted all cause mortality
  dataimpute.v23$s.cum.br5[n] <- s.cum.br[1]
  dataimpute.v23$s.cum.br10[n] <- s.cum.br[2]
  dataimpute.v23$s.cum.br15[n] <- s.cum.br[3]

  dataimpute.v23$s.cum.oth5[n] <- s.cum.oth[1]
  dataimpute.v23$s.cum.oth10[n] <- s.cum.oth[2]
  dataimpute.v23$s.cum.oth15[n] <- s.cum.oth[3]

  dataimpute.v23$all5[n] <- pred.all[1]
  dataimpute.v23$all10[n] <- pred.all[2]
  dataimpute.v23$all15[n] <- pred.all[3]


  #prognostic index, this is not related to time
  dataimpute.v23$pi[n] <- pi #larger pi is associated with higher risks of events

}
#calculate the predicted 10 years survival using PREDICT! v.2.1:

dataimpute.v23<- dataimpute.v23 %>%
  mutate(predsurv5 = 1 - all5,
         predsurv10 = 1 - all10,
         predsurv15 = 1 - all15)

Session information

sessionInfo()
## R version 4.1.3 (2022-03-10)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.6 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/liblapack.so.3
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] grid      stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] table1_1.4.3     VIM_6.2.2        colorspace_2.0-3 MASS_7.3-55     
##  [5] forcats_0.5.2    stringr_1.5.0    dplyr_1.1.1      purrr_1.0.0     
##  [9] tidyr_1.2.1      tibble_3.2.1     ggplot2_3.4.1    tidyverse_1.3.2 
## [13] plyr_1.8.8       survival_3.5-5   mice_3.15.0      readr_2.1.3     
## [17] readxl_1.4.1    
## 
## loaded via a namespace (and not attached):
##  [1] fs_1.5.2            bit64_4.0.5         lubridate_1.9.0    
##  [4] httr_1.4.4          tools_4.1.3         backports_1.4.1    
##  [7] bslib_0.4.2         utf8_1.2.2          R6_2.5.1           
## [10] DBI_1.1.3           nnet_7.3-17         withr_2.5.0        
## [13] sp_1.6-0            tidyselect_1.2.0    bit_4.0.5          
## [16] compiler_4.1.3      cli_3.5.0           rvest_1.0.3        
## [19] xml2_1.3.3          sass_0.4.4          scales_1.2.1       
## [22] DEoptimR_1.0-11     lmtest_0.9-40       robustbase_0.95-0  
## [25] proxy_0.4-27        digest_0.6.31       rmarkdown_2.19     
## [28] pkgconfig_2.0.3     htmltools_0.5.4     highr_0.10         
## [31] dbplyr_2.2.1        fastmap_1.1.0       rlang_1.1.0        
## [34] rstudioapi_0.14     jquerylib_0.1.4     generics_0.1.3     
## [37] zoo_1.8-11          jsonlite_1.8.4      vroom_1.6.0        
## [40] car_3.1-1           googlesheets4_1.0.1 magrittr_2.0.3     
## [43] Formula_1.2-4       Matrix_1.5-3        Rcpp_1.0.9         
## [46] munsell_0.5.0       fansi_1.0.3         abind_1.4-5        
## [49] lifecycle_1.0.3     stringi_1.7.8       yaml_2.3.6         
## [52] carData_3.0-5       parallel_4.1.3      crayon_1.5.2       
## [55] lattice_0.20-45     haven_2.5.1         splines_4.1.3      
## [58] hms_1.1.2           knitr_1.41          pillar_1.8.1       
## [61] ranger_0.14.1       boot_1.3-28         reprex_2.0.2       
## [64] glue_1.6.2          evaluate_0.19       data.table_1.14.6  
## [67] laeken_0.5.2        modelr_0.1.10       vcd_1.4-10         
## [70] vctrs_0.6.1         tzdb_0.3.0          cellranger_1.1.0   
## [73] gtable_0.3.1        assertthat_0.2.1    cachem_1.0.6       
## [76] xfun_0.36           broom_1.0.2         e1071_1.7-12       
## [79] class_7.3-20        googledrive_2.0.0   gargle_1.2.1       
## [82] timechange_0.1.1    ellipsis_0.3.2